1. Field of the Invention
The present invention relates to a recursive type digital filter having a feedback path.
2. Description of the Prior Art
FIG. 6 is a diagram showing a configuration of a conventional recursive type digital filter. In FIG. 6, the reference number 1 designates an input terminal through which a data item is received and inputted to the recursive type digital filter, 2 denotes a plurality of multipliers, 3 denotes a plurality of adders, 4 indicates a plurality of registers for storing data as delay values for the input data, and 5 designates an output terminal through which the data is output as output data to outside of the conventional recursive type digital filter.
Each multiplier 2 multiplies data by a coefficient in a coefficient table shown in FIG. 1. This conventional recursive type digital filter is capable of performing a 20 bit significant digit arithmetic operation.
Next, a description will now be given of the operation of the conventional recursive type digital filter shown in FIG. 6.
In general, the conventional recursive type digital filter is used for digital signal processing of audio devices, for example. This digital filter inputs an audio digital signal and performs a predetermined operation for the received audio digital data and outputs the audio digital signal without noise to external devices.
In FIG. 6, the multiplier 2 multiplies a data item such, as the input data item received through the input terminal 1, by a pre-set coefficient value that has been set previously. The input data item is added by the adder 3 and delayed in time using data stored in the register 4. Finally, the desired audio digital data item is provided through the output terminal 5 to external devices.
In addition to this feature, as shown in FIG. 6, the conventional recursive type digital filter has a feedback path. When data is received once through the input terminal 1, the operation result is fed back to the input terminal 1 through the feedback path. Thereby, the data that does not satisfy causality is output through the output terminal 5 to external devices.
Since the conventional recursive type digital filter has the configuration described above, there is a drawback in which the output data from the output terminal 5 can not converge to zero, namely, the phenomenon of a limit cycle occurs, by a rounding error caused by the operation of a limited significant digit as the 20 bit significant digit even if the input data item becomes "0".
This phenomenon will now be explained in detail by using numerical values.
Firstly, an optional data item is inputted to the input terminal 1. Secondly, the data "0" is inputted through the input terminal 1, for example. In addition, when the data as the operation result converges to zero from a positive value, the 20 bit data item is changed as follows:
000000000000000.0010 (2), PA1 000000000000000.0001 (2), and PA1 000000000000000.0000 (2). PA1 1111111111111111.1101 (2), PA1 1111111111111111.1110 (2), and PA1 1111111111111111.1111 (2),
Thus, the 20 bit data item approaches "0" at every repeating of the data output through the output terminal 5. After this, the output data converges to zero.
However, the conventional recursive type digital filter shown in FIG. 6 has a drawback that the output data item converges toward zero and converges to -1 when the output data item converges to zero from a negative value. Therefore it is difficult for the output data item to converge to zero correctly. This 20 bit data item is expressed by using a 2's complement notation as follows:
where the most significant bit indicates a sign bit.